Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
438 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×D4×Dic97 | C2 | semidirect |
| 3. C2×#15690732 | C2 | semidirect |
| 4. #20260636 | C2 | semidirect |
| 5. #20260497 | C2 | semidirect |
| 6. #20260489 | C2 | semidirect |
| 7. C2×#102×C97 | C2 | semidirect |
| 12. C2×#13095496 | C4 | semidirect |
| 32. C2×D388 | C2×C4 | semidirect |
| 42. C2×#11715895 | C2×C4 | semidirect |
| 82. D4×C97 | C22⋊C4 | semidirect |
| 101. C2×Dic97 | D8 | semidirect |
| 147. C97 | #1879 | semidirect |
| 151. C2×#102 | D97 | semidirect |
| 233. D4 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095496 | 2 |
| C2×D4×Dic97 | 2 |
| C2×#15690732 | 2 |
| #20260636 | 2 |
| #20260497 | 2 |
| #20260489 | 2 |
| C2×#102×C97 | 2 |
| #1879 | 97 |